1. Field of the Invention
The present invention relates to a method of analyzing a fringe image having separate regions. In this method, numerical data are obtained by observing fringe images such as interference fringes, moiré fringes, photoelastic fringes, and Schlieren fringes in measurement of surface forms and transmitted wavefront measurement in which forms are observed as being divided by structures, structures of objects themselves, structures of observing means, or the like, such as surface form measurement of objects having groove-like structures in relatively smooth surface forms like chuck discs, whetstones for grinding and polishing, clutch plates for automobiles, and grooved optical prisms; face measurement by use of an optical wavefront through a crisscross scale, a viewer window with a reinforcement, and moiré gratings with reference lines; and the like.
2. Description of the Prior Art
Along with the advance of industrial technology, the demand for accurately measuring objects has been increasing. Also, the product control by means of computers has advanced, whereby results of measurement of objects have been required more and more in the form of numerical values.
Measurement means includes point measurement method in which the whole is measured as an assembly of point measurements, and pattern measurement method in which the whole is measured in terms of analog information whereas the numerical value of each point is determined by image analysis.
The point measurement method is advantageous in that results are obtained as numeric values per se at the time of measurement, but it takes time if the number of measurement points increases, thereby inevitably becoming susceptible to disturbance during the measurement.
On the other hand, though the measurement time is short in the pattern measurement method, the results obtained as analog information must be converted into numerical information.
Hence, there have been attempts to carry out efficient inspection/measurement by combining the point measurement and pattern measurement together in the industry. For an optical lens, by way of example, the point measurement is employed for inspecting its center thickness and outer diameter, whereas the pattern measurement is employed when it is necessary to finely inspect the whole surface as in surface form inspection and material density inspection.
A typical example of the pattern measurement is fringe image measurement represented by interference fringes and moiré fringes. The fringe analysis method in which the numerical information of each point is determined from a fringe image has become easy to carry out thanks to computers, the increase in their memory in particular.
Typical examples of fringe analysis method include the fringe-thinning method described in “Applied Optics—Introduction to Optical Measurement,” pp. 185-195, published by Maruzen Co., Ltd., and the phase shift fringe analysis method (also known as fringe scanning method or phase scanning method) described in “PHASE-MEASUREMENT INTERFEROMETRY TECHNIQUES,” PROGRESS IN OPTICS, Vol. XXXVI (1988), pp. 349-393.
The above-mentioned fringe-thinning method thins a fringe having a gradation in a fringe image by binary-coding at its peak position, calculates the ordinal number of each point in the fringe image with reference to its surrounding thinned fringe patterns, and multiplies it by a sensitivity per fringe stripe, thereby determining numerical values of all the points of the fringe image.
The phase-shift fringe analysis method measures changes in brightness in all the points of the fringe image in the process of scanning one stripe of the fringe pattern, and calculates the phase of each point from its results, thereby determining numerical values of all the points of the fringe image.
In each of the above-mentioned fringe analysis methods, analyzable patterns are limited to those which are at least partly continuous, whereby fringe patterns occurring in a plurality of regions which are completely separated from each other by grooves and the like have been hard to analyze as a total of the plurality of regions even though the individual regions can discretely be taken out and analyzed.
On the other hand, a method in which a phase calculation of each independent region is carried out and then the respective phases of separate regions are fitted in terms of least squares so as to provide each separate region with a phase relationship is described in Hiroaki Takajo and Tohru Takahashi, “Least-squares phase estimation from the phase difference,” J.O.S.A. A/Vol. 5, No. 3, March 1988, pp. 416-425.
The above-mentioned technique of fitting a wavefront in terms of least squares is quite effective against dust and dirt, vibrations, turbulence in air, and the like at the time of phase unwrapping as in amplitude-maximizing method, an execution condition for enabling the phase unwrapping will additionally be necessary if there is an independent start point for connecting phases because of the fact that separate regions exist. Also, it is necessary for this method to individually look for start points for connecting phases with respect to separate regions, so as to unwrap each separate region, estimate a phase of the whole by least squares thereafter, and then determine the phase of each separate region after arranging the independent start point for connecting phases into a phase difference of an integer multiple of 2π, thereby necessitating a quite complicated calculation and taking a long analysis time.
Meanwhile, in an inspection area separated into a plurality of independent regions by suction grooves as in a surface of a chuck disc for chucking a wafer in the making of IC, there has been a strong demand in the industry for measuring with a high accuracy not only the respective surface forms of individual independent regions but also the surface form of the whole constituted by these independent regions. In mass-products such as grooved optical prisms, in particular, there has been a strong demand for shortening the measurement time since it greatly affects their cost and quantity of production.